Fixing Briffa’s Latest
Posted by Jeff Id on November 1, 2009
This is a very difficult post for me because I don’t believe any of this has anything to do with temperature, however some well paid scientists disagree. This is therefore in response to a Keith Briffa pre-paper replying to SteveM’s post on Yamal where he replaced some of the data using a Schweingruber dataset. Briffa presented what he referred to as a sensitivity test of Yamal by adding different datasets in. While he didn’t provide his code, he did provide the data and plots of the RCS corrections applied to the various datasets.
RCS is a generic method of fitting a curve to a set of tree ring data. In the original Yamal an exponential decay was used to represent tree ring widths. I’m critical of the exponential function method because it doesn’t recognize the potential for trees to increase in growth rate as they age. Since nothing I’ve read biologically defines that this is impossible it makes no sense to ignore the possibility unless you want older trees to curve upward after standardization. It’s odd to see it being ignored by the pros but it happens to result in spurious hockey sticks through a complex and surprisingly common mathematical phenomena referred to here as hockestickization.
Yamal is a driver amongst hockey sticks – I mean a good old fashion 1 wood. Straight shaft, sharp blade, wide sweet spot. Since Steve’s discovery the climatoknowledgists have been scrambling to explain how so few trees could define such strong warming around the globe. In Briffa’s response he showed several methods using new data to also create hockey sticks. However, Dr. Briffa again used a method which is functionally identical to the exponential decay method for correcting tree ring widths. It seems he simply cannot recognize that trees may increase in ring width.
You can see that the bottom pane has a variety of curves which all have an uptrend similar to the original Yamal. Briffa did one nice thing in that he didn’t repeat Dr. Tom P’s mistake of including Yamal only years in the data. If the sensitivity data ends early, Briffa correctly ended the comparison curves early. When this story first broke, Tom P argued that Steve McIntyre had failed to do his sensitivity analysis correctly but in fact Tom had mistakenly extended the Yamal data past the sensitivity data. My reply was here. I never did read an admission of error from him on that one.
Anyway, note the curves used for correcting the datasets. They are very similar to the exponential curves used to create the original Yamal emulated in this next figure. Before I continue, much of this post was created from code written and published by Steve McIntyre although I’ve made many changes so mistakes are my own.
The last pane of the above figure shows the Yamal hockey stick, the middle pane shows that not many trees were used in recent years to make it. My problem with it is addressed here and that is the exponential curve in the top pane of the above 3 graphs. The curve doesn’t follow the average tree age which trends upward after about 200 years. Since the middle of the series has both young and old trees overlapping, standardization problems average out. This means that errors in standardization will only have a real effect on either end. The problem for RCS is therefore summarized like this:
1 – Standardization affects only ends of chronologies
2 – Trees grow at a variable average rate even in the same climate conditions. This rate is manifested in variable ring widths.
3 – Trees often grow faster after a certain age when competition is beaten and resources are monopolized.
4 – Old trees are easier to find when alive, fossil and subfossil records will tend toward a younger age.
5 – Exponential decay does not correct for increasing growth in later years.
The result then is an uptick at the end of the RCS chronology created by the math. So this post attempts to fix this one aspect of the Yamal series. There are a bunch of graphs to show but the point is pretty simple. I used a spline correction similar to the Esper method, fitting the data to the mean ring width for the various new trees from Briffa.
OK, now the RUSS series is the Schweingruber series that SteveM used in the Yamal data. Instead of playing around with a boring sensitivity test I combined all of the data into full chronologies a couple of different ways using the maximum amount of data. Before we move on, look at the age of the trees in the first pane of each chronology. Several follow a nice exponential drop until about 200 years followed by a rise later on. There are a couple who don’t follow a nice curve like that, I’m not sure why but the point is that RCS needs the ability to fit the rise and a pure exponential decay doesn’t allow for that. A second issue you’ll notice is that older trees have a lot of variation in ring width. The signal goes wild as trees age. This could be due to less old trees in the series but it is a noticeable effect.
First, I looked at an average of the above series after correction by spline.
The red line is the new chronology. As I explained above the only real differences created by different RCS methods occur at the ends of the chronology.The huge spike at the end is reduced from the original Yamal but is still positive. The next graph is a zoomed in version which if it were temperature, the red line would probably be a better match to measured data than the original black. However, IMO it isn’t temperature.
The next graph is the same data as the above with a 5 year filter instead of a 21 year. It’s almost always better to look at endpoints with less filtering because the ends are affected by the assumptions. So, for those who see temperature in these things, what about this?
We have just removed any resemblance to the hockey sticks from from Yamal by using all the data. This isn’t any less valid than Briffa’s versions.
But wait, I’ve got another version. The above reconstruction uses a different RCS spline fit for each region, there certainly is an argument for that method but the resulting average isn’t weighted according to the number of trees so a series with 10 trees has the same weight as one with 25. I took all the data together and did a single RCS spline fit.
The reconstruction is the bottom pane. Great Jeff you made your own hockey stick, nice work right? You can see the huge core count in recent years right before the blade happens. The blade in this case though deserves a closer look.
This is the unfiltered version.
You can see the blade is very thin in reality. The whole series ends in 1996 so I chopped one year (ONE SINGLE VALUE ON THE END) to see the difference.
Now visually that’s a significant difference from the previous pane yet it’s only chopping a single value from 1996. There were 19 cores in 1996 but in 1994 there were 42. I’m certain that the lack of new and young trees has a lot to do with the unprecedented nature of the spike. You can just look at the lack of variance in the early portion of the curve fit’s (pane 1) in the above chronologies (fig 3, 4,5,6 …) and it becomes very apparent that it would be almost 100% impossible for a group of young trees to make a 3 sigma deviation from the mean of the curve.
I hope that makes sense, it’s what drives me nuts about this treemometer stuff. It just ain’t science.
Anyway, our eyes tend to focus on the big bladey looking bit at the end without realizing just how narrow it really is. Here’s a filtered versioin truncated only 5 years to 1990. I picked 1990 because that’s the year that the data availability jumped up to over 80 cores.
The entire 19th century using all the data is now one of the coolest on record!!
My conclusion is that there is no REAL uptick in Yamal. There are methods which show an uptick but the number of cores is still low. For the uptick to be continuous for 100ish years as corrected HadCRUT temperature is you need to have an RCS which creates a continuous upslope like exponential RCS. What bugs me so much about that is that this continuous slope is just about all that is required for correlation to temp.
No matter how you see the last 3 graphs, they sure as heck don’t look like temp. It’s my contention that they are of equal quality to Briffa’s original Yamal. This post took a long time because there were hundreds of other plots I could have shown and have done, but there are enough plots here for the serious to figure out what’s going on.